Subgroups — C₆₁×#19966 #29523399

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3400	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3396	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1686	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1668	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1640	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1626	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#559	C₂²	1	2	yes	—
13	C₆₁×#557	C₂²	1	2	yes	—
14	C₆₁×#500	C₂²	1	1	yes	characteristic
15	C₆₁×#499	—	2	1	no	—
16	C₆₁×#497	—	2	2	no	—
17	C₆₁×#495	—	2	1	no	—
18	C₆₁×#493	C₂²	1	1	yes	characteristic
19	C₆₁×#492	C₂²	1	2	yes	—
20	C₆₁×#486	C₂²	1	2	yes	—
21	C₆₁×#479	—	2	2	no	—
22	C₆₁×#475	C₂²	1	2	yes	—
23	C₆₁×#464	—	2	2	no	—
24	C₆₁×#463	—	2	2	no	—
25	C₆₁×#462	C₂²	1	2	yes	—
26	C₆₁×#461	—	2	2	no	—
27	C₆₁×#460	C₂²	1	2	yes	—
28	C₆₁×#460	C₂²	1	2	yes	—
29	C₆₁×#446	C₂²	1	2	yes	—
30	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#440	—	2	2	no	—
33	C₄×Q₁₆×C₆₁	—	2	1	no	—
34	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₆₁	—	2	1	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#335	C₂²	1	1	yes	characteristic
39	C₆₁×#332	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₁	—	2	2	no	—
46	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×D₈×C₆₁	—	2	1	no	—
53	C₂×D₈×C₆₁	—	2	1	no	—
54	C₄⋊Q₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
56	#127×C₆₁	C₂³	1	2	yes	—
57	#125×C₆₁	—	2	2	no	—
58	#125×C₆₁	—	4	2	no	—
59	#124×C₆₁	—	2	2	no	—
60	#124×C₆₁	—	2	2	no	—
61	#123×C₆₁	—	4	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	—	2	2	no	—
64	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
66	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₆₁	—	2	2	no	—
68	C₄×D₄×C₆₁	—	2	2	no	—
69	#107×C₆₁	—	2	1	no	—
70	#107×C₆₁	—	2	1	no	—
71	#107×C₆₁	D₄	1	1	yes	characteristic
72	#107×C₆₁	D₄	1	1	yes	characteristic
73	#106×C₆₁	—	2	2	no	—
74	C₄⋊C₈×C₆₁	—	2	1	no	—
75	C₄⋊C₈×C₆₁	—	2	1	no	—
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
80	#103×C₆₁	—	2	2	no	—
81	#103×C₆₁	—	2	2	no	—
82	#103×C₆₁	D₄	1	1	yes	characteristic
83	#103×C₆₁	D₄	1	2	yes	—
84	#103×C₆₁	D₄	1	1	yes	characteristic
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	4	2	no	—
88	#97×C₆₁	—	2	2	no	—
89	C₄×C₈×C₆₁	—	2	1	no	—
90	C₄×C₈×C₆₁	—	2	1	no	—
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
96	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	4	2	no	—
102	Q₁₆×C₆₁	—	2	2	no	—
103	Q₁₆×C₆₁	—	2	2	no	—
104	Q₁₆×C₆₁	—	8	2	no	—
105	SD₁₆×C₆₁	—	4	4	no	—
106	SD₁₆×C₆₁	—	8	2	no	—
107	SD₁₆×C₆₁	—	8	2	no	—
108	SD₁₆×C₆₁	—	8	2	no	—
109	D₈×C₆₁	—	4	2	no	—
110	D₈×C₆₁	—	8	1	no	—
111	C₂×C₈×C₆₁	—	2	1	no	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₆₁	—	2	1	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	1	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	4	2	no	—
125	C₄⋊C₄×C₆₁	—	4	2	no	—
126	C₄⋊C₄×C₆₁	—	4	2	no	—
127	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂²⋊C₄×C₆₁	—	4	2	no	—
131	C₂²⋊C₄×C₆₁	—	4	2	no	—
132	C₂²⋊C₄×C₆₁	—	4	2	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₄²×C₆₁	—	2	2	no	—
136	C₄²×C₆₁	—	4	2	no	—
137	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₂³×C₆₁	—	4	2	no	—
139	Q₈×C₆₁	—	2	1	no	—
140	Q₈×C₆₁	—	2	1	no	—
141	Q₈×C₆₁	—	2	2	no	—
142	Q₈×C₆₁	—	2	1	no	—
143	Q₈×C₆₁	—	2	1	no	—
144	Q₈×C₆₁	—	2	2	no	—
145	Q₈×C₆₁	—	4	2	no	—
146	Q₈×C₆₁	—	4	2	no	—
147	D₄×C₆₁	—	4	2	no	—
148	D₄×C₆₁	—	4	2	no	—
149	D₄×C₆₁	—	4	2	no	—
150	D₄×C₆₁	—	4	2	no	—
151	D₄×C₆₁	—	8	2	no	—
152	C₂×C₄×C₆₁	—	2	1	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	16	2	no	—
160	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₈×C₆₁	—	2	1	no	—
164	C₈×C₆₁	—	2	1	no	—
165	C₈×C₆₁	—	4	1	no	—
166	C₈×C₆₁	—	4	2	no	—
167	C₈×C₆₁	—	4	1	no	—
168	C₈×C₆₁	—	4	1	no	—
169	C₈×C₆₁	#135	1	2	yes	—
170	C₈×C₆₁	#137	1	2	yes	—
171	#19966	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₆₁	—	8	2	no	—
173	C₂²×C₆₁	—	8	2	no	—
174	C₂²×C₆₁	—	8	2	no	—
175	C₂²×C₆₁	D₄²	1	1	yes	characteristic
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	4	2	no	—
178	C₄×C₆₁	—	4	1	no	—
179	C₄×C₆₁	—	4	1	no	—
180	C₄×C₆₁	—	4	1	no	—
181	C₄×C₆₁	—	4	2	no	—
182	C₄×C₆₁	—	4	1	no	—
183	C₄×C₆₁	—	8	2	no	—
184	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
185	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
186	C₄×C₆₁	#576	1	1	yes	characteristic
187	C₄×C₆₁	#577	1	1	yes	characteristic
188	#3400	C₂×C₆₁	1	2	yes	complemented
189	#3396	C₂×C₆₁	1	1	yes	characteristic
190	#3383	C₂×C₆₁	1	1	yes	characteristic, complemented
191	#1706	C₂×C₆₁	1	1	yes	characteristic
192	#1686	C₂×C₆₁	1	2	yes	complemented
193	#1674	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#1668	C₂×C₆₁	1	1	yes	characteristic
195	#1640	C₂×C₆₁	1	2	yes	complemented
196	#1626	C₂×C₆₁	1	2	yes	complemented
197	#1591	C₂×C₆₁	1	1	yes	characteristic, complemented
198	C₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
199	C₂×C₆₁	—	16	2	no	—
200	C₂×C₆₁	#3278	1	1	yes	characteristic
201	C₂×C₆₁	#3287	1	1	yes	characteristic
202	C₂×C₆₁	#3290	1	1	yes	characteristic
203	#559	C₂²×C₆₁	1	2	yes	—
204	#557	C₂²×C₆₁	1	2	yes	—
205	#500	C₂²×C₆₁	1	1	yes	characteristic
206	#499	—	2	1	no	—
207	#497	—	2	2	no	—
208	#495	—	2	1	no	—
209	#493	C₂²×C₆₁	1	1	yes	characteristic
210	#492	C₂²×C₆₁	1	2	yes	—
211	#486	C₂²×C₆₁	1	2	yes	—
212	#479	—	2	2	no	—
213	#475	C₂²×C₆₁	1	2	yes	—
214	#464	—	2	2	no	—
215	#463	—	2	2	no	—
216	#462	C₂²×C₆₁	1	2	yes	—
217	#461	—	2	2	no	—
218	#460	C₂²×C₆₁	1	2	yes	—
219	#460	C₂²×C₆₁	1	2	yes	—
220	#446	C₂²×C₆₁	1	2	yes	—
221	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
222	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
223	#440	—	2	2	no	—
224	C₄×Q₁₆	—	2	1	no	—
225	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
226	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
227	C₄×D₈	—	2	1	no	—
228	#335	C₂²×C₆₁	1	1	yes	characteristic
229	#335	C₂²×C₆₁	1	1	yes	characteristic
230	#332	C₂²×C₆₁	1	2	yes	—
231	#331	C₂²×C₆₁	1	2	yes	—
232	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
233	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
234	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
235	C₈²	C₂²×C₆₁	1	1	yes	characteristic
236	C₆₁	#19966	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
239	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
248	#127	C₂³×C₆₁	1	2	yes	—
249	#125	—	2	2	no	—
250	#125	—	4	2	no	—
251	#124	—	2	2	no	—
252	#124	—	2	2	no	—
253	#123	—	4	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
257	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
258	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	D₄×C₆₁	1	1	yes	characteristic
264	#107	D₄×C₆₁	1	1	yes	characteristic
265	#106	—	2	2	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
270	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
271	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
272	#103	—	2	2	no	—
273	#103	—	2	2	no	—
274	#103	D₄×C₆₁	1	1	yes	characteristic
275	#103	D₄×C₆₁	1	2	yes	—
276	#103	D₄×C₆₁	1	1	yes	characteristic
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	4	2	no	—
280	#97	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
288	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	8	2	no	—
297	SD₁₆	—	4	4	no	—
298	SD₁₆	—	8	2	no	—
299	SD₁₆	—	8	2	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	4	2	no	—
302	D₈	—	8	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
321	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
330	C₂³	—	4	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	8	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	16	2	no	—
352	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
354	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	4	1	no	—
358	C₈	—	4	2	no	—
359	C₈	—	4	1	no	—
360	C₈	—	4	1	no	—
361	C₈	#135×C₆₁	1	2	yes	—
362	C₈	#137×C₆₁	1	2	yes	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	D₄²×C₆₁	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
376	C₄	C₂×#137×C₆₁	1	1	yes	characteristic
377	C₄	C₆₁×#576	1	1	yes	characteristic
378	C₄	C₆₁×#577	1	1	yes	characteristic
379	C₂	—	16	2	no	—
380	C₂	C₆₁×#3278	1	1	yes	characteristic
381	C₂	C₆₁×#3287	1	1	yes	characteristic
382	C₂	C₆₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#493	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₁×#3400	C₂	semidirect
3. C₆₁×#3383	C₂	semidirect
5. C₆₁×#1686	C₂	semidirect
6. C₆₁×#1674	C₂	semidirect
8. C₆₁×#1640	C₂	semidirect
9. C₆₁×#1626	C₂	semidirect
10. C₆₁×#1591	C₂	semidirect
11. C₈×Q₁₆×C₆₁	C₂	semidirect
171. #19966	C₆₁	direct (N × H)
188. #3400	C₂×C₆₁	semidirect
190. #3383	C₂×C₆₁	semidirect
192. #1686	C₂×C₆₁	semidirect
193. #1674	C₂×C₆₁	semidirect
195. #1640	C₂×C₆₁	semidirect
196. #1626	C₂×C₆₁	semidirect
197. #1591	C₂×C₆₁	semidirect
198. C₈×Q₁₆	C₂×C₆₁	semidirect
236. C₆₁	#19966	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3400	2
C₆₁×#3396	2
C₆₁×#3383	2
C₆₁×#1706	2
C₆₁×#1686	2
C₆₁×#1674	2
C₆₁×#1668	2
C₆₁×#1640	2
C₆₁×#1626	2
C₆₁×#1591	2
C₈×Q₁₆×C₆₁	2
#19966	61

Subgroups — C61×#19966 #29523399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19966 #29523399